臺灣博碩士論文加值系統

　　分析具有巢狀誤差結構的迴歸模式時，若忽略隨機誤差項之間的相關性，而採用最小平方(OLS)估計量所導出的標準E統計量（以Fs表之）進行檢定，會導致過大的型I錯誤機率；若將隨機誤差項之間的相關性納入考量，而採用廣義最小平方(GLS)估計量所導出的F統計量（以FGLS表之），則計算上會較為繁雜。因此我們藉由轉換方式，將模式轉換成隨機誤差項之間彼此獨立的新模式後，再以Fs進行檢定，其結果與直接以FGLS檢定相同，且可使計算較為方便。由於模式轉換所需的轉換矩陣為母體變異數的函數，因此當母體變異數未知時，我們以Henderson的常數配適(fitting-of-constants)方法來估計之。藉由模擬結果得知，若各段的觀察個數相等，則不論巢狀誤差結構為二段式(two-stage)或三段式(three-stage)，廣義最小平方估計量(GLS)均較最小平方估計量(OLS)表現穩定，且FGLS在檢定力及實際顯著水準方面的表現也都比Fs好。

　　When analyzing the regression model with nested-error structure, if the correlations between errors are ignored, and conducting the model adequacy test by the standard F statistic (Fs) led from the ordinary leastsquares estimator (OLSE), then the type I error rate will be inflated. However, if the correlated structure is considered and the model is tested by FGLS led from the general least-squares estimator (GLSE), the calculation will be more complicate. The model can be transformed to a new model with independent rando errors and then, tested by Fs. The result is the same as the one by FGLS, also it is more convenient for calculation. Since the transformation matrix is a function of variance components, we estimate variance components by Henderson's fitting-of-constants when they are unknown. Through simulation, it is concluded that if the observations in each stage of nested-error structure are the same, the GLSE is more stable than the OLSE in both two-stage and three-stage structures. Also, the power and the sizes of FGLS will perform better than those of Fs.